{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probabilistic Matrix Factorization for Making Personalized Recommendations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running on PyMC3 v3.8\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import pymc3 as pm\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "plt.style.use('seaborn-darkgrid')\n",
    "print('Running on PyMC3 v{}'.format(pm.__version__))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Motivation\n",
    "\n",
    "So you are browsing for something to watch on Netflix and just not liking the suggestions. You just know you can do better. All you need to do is collect some ratings data from yourself and friends and build a recommendation algorithm. This notebook will guide you in doing just that!\n",
    "\n",
    "We'll start out by getting some intuition for how our model will work. Then we'll formalize our intuition. Afterwards, we'll examine the dataset we are going to use. Once we have some notion of what our data looks like, we'll define some baseline methods for predicting preferences for movies. Following that, we'll look at Probabilistic Matrix Factorization (PMF), which is a more sophisticated Bayesian method for predicting preferences. Having detailed the PMF model, we'll use PyMC3 for MAP estimation and MCMC inference. Finally, we'll compare the results obtained with PMF to those obtained from our baseline methods and discuss the outcome.\n",
    "\n",
    "## Intuition\n",
    "\n",
    "Normally if we want recommendations for something, we try to find people who are similar to us and ask their opinions. If Bob, Alice, and Monty are all similar to me, and they all like crime dramas, I'll probably like crime dramas. Now this isn't always true. It depends on what we consider to be \"similar\". In order to get the best bang for our buck, we really want to look for people who have the most similar taste. Taste being a complex beast, we'd probably like to break it down into something more understandable. We might try to characterize each movie in terms of various factors. Perhaps films can be moody, light-hearted, cinematic, dialogue-heavy, big-budget, etc. Now imagine we go through IMDB and assign each movie a rating in each of the categories. How moody is it? How much dialogue does it have? What's its budget? Perhaps we use numbers between 0 and 1 for each category. Intuitively, we might call this the film's profile.\n",
    "\n",
    "Now let's suppose we go back to those 5 movies we rated. At this point, we can get a richer picture of our own preferences by looking at the film profiles of each of the movies we liked and didn't like. Perhaps we take the averages across the 5 film profiles and call this our ideal type of film. In other words, we have computed some notion of our inherent _preferences_ for various types of movies. Suppose Bob, Alice, and Monty all do the same. Now we can compare our preferences and determine how similar each of us really are. I might find that Bob is the most similar and the other two are still more similar than other people, but not as much as Bob. So I want recommendations from all three people, but when I make my final decision, I'm going to put more weight on Bob's recommendation than those I get from Alice and Monty.\n",
    "\n",
    "While the above procedure sounds fairly effective as is, it also reveals an unexpected additional source of information. If we rated a particular movie highly, and we know its film profile, we can compare with the profiles of other movies. If we find one with very close numbers, it is probable we'll also enjoy this movie. Both this approach and the one above are commonly known as _neighborhood approaches_. Techniques that leverage both of these approaches simultaneously are often called _collaborative filtering_ [[1]](http://www2.research.att.com/~volinsky/papers/ieeecomputer.pdf). The first approach we talked about uses user-user similarity, while the second uses item-item similarity. Ideally, we'd like to use both sources of information. The idea is we have a lot of items available to us, and we'd like to work together with others to filter the list of items down to those we'll each like best. My list should have the items I'll like best at the top and those I'll like least at the bottom. Everyone else wants the same. If I get together with a bunch of other people, we all watch 5 movies, and we have some efficient computational process to determine similarity, we can very quickly order the movies to our liking.\n",
    "\n",
    "## Formalization\n",
    "\n",
    "Let's take some time to make the intuitive notions we've been discussing more concrete. We have a set of $M$ movies, or _items_ ($M = 100$ in our example above). We also have $N$ people, whom we'll call _users_ of our recommender system. For each item, we'd like to find a $D$ dimensional factor composition (film profile above) to describe the item. Ideally, we'd like to do this without actually going through and manually labeling all of the movies. Manual labeling would be both slow and error-prone, as different people will likely label movies differently. So we model each movie as a $D$ dimensional vector, which is its latent factor composition. Furthermore, we expect each user to have some preferences, but without our manual labeling and averaging procedure, we have to rely on the latent factor compositions to learn $D$ dimensional latent preference vectors for each user. The only thing we get to observe is the $N \\times M$ ratings matrix $R$ provided by the users. Entry $R_{ij}$ is the rating user $i$ gave to item $j$. Many of these entries may be missing, since most users will not have rated all 100 movies. Our goal is to fill in the missing values with predicted ratings based on the latent variables $U$ and $V$. We denote the predicted ratings by $R_{ij}^*$. We also define an indicator matrix $I$, with entry $I_{ij} = 0$ if $R_{ij}$ is missing and $I_{ij} = 1$ otherwise.\n",
    "\n",
    "So we have an $N \\times D$ matrix of user preferences which we'll call $U$ and an $M \\times D$ factor composition matrix we'll call $V$. We also have a $N \\times M$ rating matrix we'll call $R$. We can think of each row $U_i$ as indications of how much each user prefers each of the $D$ latent factors. Each row $V_j$ can be thought of as how much each item can be described by each of the latent factors. In order to make a recommendation, we need a suitable prediction function which maps a user preference vector $U_i$ and an item latent factor vector $V_j$ to a predicted ranking. The choice of this prediction function is an important modeling decision, and a variety of prediction functions have been used. Perhaps the most common is the dot product of the two vectors, $U_i \\cdot V_j$ [[1]](http://www2.research.att.com/~volinsky/papers/ieeecomputer.pdf).\n",
    "\n",
    "To better understand CF techniques, let us explore a particular example. Imagine we are seeking to recommend movies using a model which infers five latent factors, $V_j$, for $j = 1,2,3,4,5$. In reality, the latent factors are often unexplainable in a straightforward manner, and most models make no attempt to understand what information is being captured by each factor.  However, for the purposes of explanation, let us assume the five latent factors might end up capturing the film profile we were discussing above. So our five latent factors are: moody, light-hearted, cinematic, dialogue, and budget. Then for a particular user $i$, imagine we infer a preference vector $U_i = <0.5, 0.1, 1.5, 1.1, 0.3>$. Also, for a particular item $j$, we infer these values for the latent factors: $V_j = <0.5, 1.5, 1.25, 0.8, 0.9>$. Using the dot product as the prediction function, we would calculate 3.425 as the ranking for that item, which is more or less a neutral preference given our 1 to 5 rating scale.\n",
    "\n",
    "$$ 0.5 \\times 0.5 + 0.1 \\times 1.5 + 1.5 \\times 1.25 + 1.1 \\times 0.8 + 0.3 \\times 0.9 = 3.425 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data\n",
    "\n",
    "The [MovieLens 100k dataset](https://grouplens.org/datasets/movielens/100k/) was collected by the GroupLens Research Project at the University of Minnesota. This data set consists of 100,000 ratings (1-5) from 943 users on 1682 movies. Each user rated at least 20 movies, and be have basic information on the users (age, gender, occupation, zip). Each movie includes basic information like title, release date, video release date, and genre. We will implement a model that is suitable for collaborative filtering on this data and evaluate it in terms of root mean squared error (RMSE) to validate the results.\n",
    "\n",
    "The data was collected through the MovieLens web site\n",
    "(movielens.umn.edu) during the seven-month period from September 19th,\n",
    "1997 through April 22nd, 1998. This data has been cleaned up - users\n",
    "who had less than 20 ratings or did not have complete demographic\n",
    "information were removed from this data set.\n",
    "\n",
    "\n",
    "Let's begin by exploring our data. We want to get a general feel for what it looks like and a sense for what sort of patterns it might contain. Here are the user rating data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>userid</th>\n",
       "      <th>itemid</th>\n",
       "      <th>rating</th>\n",
       "      <th>timestamp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>196</td>\n",
       "      <td>242</td>\n",
       "      <td>3</td>\n",
       "      <td>881250949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>186</td>\n",
       "      <td>302</td>\n",
       "      <td>3</td>\n",
       "      <td>891717742</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>22</td>\n",
       "      <td>377</td>\n",
       "      <td>1</td>\n",
       "      <td>878887116</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>244</td>\n",
       "      <td>51</td>\n",
       "      <td>2</td>\n",
       "      <td>880606923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>166</td>\n",
       "      <td>346</td>\n",
       "      <td>1</td>\n",
       "      <td>886397596</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   userid  itemid  rating  timestamp\n",
       "0     196     242       3  881250949\n",
       "1     186     302       3  891717742\n",
       "2      22     377       1  878887116\n",
       "3     244      51       2  880606923\n",
       "4     166     346       1  886397596"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(pm.get_data(\"ml_100k_u.data\"), sep='\\t', names=[\"userid\", \"itemid\", \"rating\", \"timestamp\"])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here is the movie detail data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>movie title</th>\n",
       "      <th>release date</th>\n",
       "      <th>video release date</th>\n",
       "      <th>IMDb URL</th>\n",
       "      <th>unknown</th>\n",
       "      <th>Action</th>\n",
       "      <th>Adventure</th>\n",
       "      <th>Animation</th>\n",
       "      <th>Children's</th>\n",
       "      <th>Comedy</th>\n",
       "      <th>...</th>\n",
       "      <th>Fantasy</th>\n",
       "      <th>Film-Noir</th>\n",
       "      <th>Horror</th>\n",
       "      <th>Musical</th>\n",
       "      <th>Mystery</th>\n",
       "      <th>Romance</th>\n",
       "      <th>Sci-Fi</th>\n",
       "      <th>Thriller</th>\n",
       "      <th>War</th>\n",
       "      <th>Western</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>movie id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Toy Story (1995)</td>\n",
       "      <td>1995-01-01</td>\n",
       "      <td>NaN</td>\n",
       "      <td>http://us.imdb.com/M/title-exact?Toy%20Story%2...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>GoldenEye (1995)</td>\n",
       "      <td>1995-01-01</td>\n",
       "      <td>NaN</td>\n",
       "      <td>http://us.imdb.com/M/title-exact?GoldenEye%20(...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Four Rooms (1995)</td>\n",
       "      <td>1995-01-01</td>\n",
       "      <td>NaN</td>\n",
       "      <td>http://us.imdb.com/M/title-exact?Four%20Rooms%...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Get Shorty (1995)</td>\n",
       "      <td>1995-01-01</td>\n",
       "      <td>NaN</td>\n",
       "      <td>http://us.imdb.com/M/title-exact?Get%20Shorty%...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Copycat (1995)</td>\n",
       "      <td>1995-01-01</td>\n",
       "      <td>NaN</td>\n",
       "      <td>http://us.imdb.com/M/title-exact?Copycat%20(1995)</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 23 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                movie title release date  video release date  \\\n",
       "movie id                                                       \n",
       "1          Toy Story (1995)   1995-01-01                 NaN   \n",
       "2          GoldenEye (1995)   1995-01-01                 NaN   \n",
       "3         Four Rooms (1995)   1995-01-01                 NaN   \n",
       "4         Get Shorty (1995)   1995-01-01                 NaN   \n",
       "5            Copycat (1995)   1995-01-01                 NaN   \n",
       "\n",
       "                                                   IMDb URL  unknown  Action  \\\n",
       "movie id                                                                       \n",
       "1         http://us.imdb.com/M/title-exact?Toy%20Story%2...        0       0   \n",
       "2         http://us.imdb.com/M/title-exact?GoldenEye%20(...        0       1   \n",
       "3         http://us.imdb.com/M/title-exact?Four%20Rooms%...        0       0   \n",
       "4         http://us.imdb.com/M/title-exact?Get%20Shorty%...        0       1   \n",
       "5         http://us.imdb.com/M/title-exact?Copycat%20(1995)        0       0   \n",
       "\n",
       "          Adventure  Animation  Children's  Comedy  ...  Fantasy  Film-Noir  \\\n",
       "movie id                                            ...                       \n",
       "1                 0          1           1       1  ...        0          0   \n",
       "2                 1          0           0       0  ...        0          0   \n",
       "3                 0          0           0       0  ...        0          0   \n",
       "4                 0          0           0       1  ...        0          0   \n",
       "5                 0          0           0       0  ...        0          0   \n",
       "\n",
       "          Horror  Musical  Mystery  Romance  Sci-Fi  Thriller  War  Western  \n",
       "movie id                                                                     \n",
       "1              0        0        0        0       0         0    0        0  \n",
       "2              0        0        0        0       0         1    0        0  \n",
       "3              0        0        0        0       0         1    0        0  \n",
       "4              0        0        0        0       0         0    0        0  \n",
       "5              0        0        0        0       0         1    0        0  \n",
       "\n",
       "[5 rows x 23 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "movie_columns  = ['movie id', 'movie title', 'release date', 'video release date', 'IMDb URL', \n",
    "                  'unknown','Action','Adventure', 'Animation',\"Children's\", 'Comedy', 'Crime',\n",
    "                  'Documentary', 'Drama', 'Fantasy', 'Film-Noir', 'Horror', 'Musical', 'Mystery',\n",
    "                  'Romance', 'Sci-Fi', 'Thriller', 'War', 'Western']\n",
    "movies = pd.read_csv(pm.get_data(\"ml_100k_u.item\"), sep=\"|\", names=movie_columns, index_col=\"movie id\", parse_dates=['release date'])\n",
    "movies.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Extract the ratings from the DataFrame\n",
    "ratings = data.rating\n",
    "\n",
    "# Plot histogram\n",
    "data.groupby('rating').size().plot(kind='bar');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    100000.000000\n",
       "mean          3.529860\n",
       "std           1.125674\n",
       "min           1.000000\n",
       "25%           3.000000\n",
       "50%           4.000000\n",
       "75%           4.000000\n",
       "max           5.000000\n",
       "Name: rating, dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.rating.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This must be a decent batch of movies. From our exploration above, we know most ratings are in the range 3 to 5, and positive ratings are more likely than negative ratings. Let's look at the means for each movie to see if we have any particularly good (or bad) movie here.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "movie_means = data.join(movies['movie title'], on='itemid').groupby('movie title').rating.mean()\n",
    "movie_means[:50].plot(kind='bar', grid=False, figsize=(16, 6),\n",
    "                      title=\"Mean ratings for 50 movies\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While the majority of the movies generally get positive feedback from users, there are definitely a few that stand out as bad. Let's take a look at the worst and best movies, just for fun:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(16, 4), sharey=True)\n",
    "movie_means.nlargest(30).plot(kind='bar', ax=ax1,title=\"Top 30 movies in data set\");\n",
    "movie_means.nsmallest(30).plot(kind='bar', ax=ax2,title=\"Bottom 30 movies in data set\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make sense to me. We now know there are definite popularity differences between the movies. Some of them are simply better than others, and some are downright lousy. Looking at the movie means allowed us to discover these general trends. Perhaps there are similar trends across users. It might be the case that some users are simply more easily entertained than others. Let's take a look."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "user_means = data.groupby('userid').rating.mean().sort_values()\n",
    "_, ax = plt.subplots(figsize=(16, 6))\n",
    "ax.plot(np.arange(len(user_means)), user_means.values, 'k-')\n",
    "\n",
    "ax.fill_between(np.arange(len(user_means)), user_means.values, alpha=0.3)\n",
    "ax.set_xticklabels('');  # 1000 labels is nonsensical\n",
    "ax.set_ylabel('Rating')\n",
    "ax.set_xlabel(f'{len(user_means)} average ratings per user')\n",
    "ax.set_ylim(0, 5)\n",
    "ax.set_xlim(0, len(user_means));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see even more significant trends here. Some users rate nearly everything highly, and some (though not as many) rate nearly everything negatively. These observations will come in handy when considering models to use for predicting user preferences on unseen movies."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Methods\n",
    "\n",
    "Having explored the data, we're now ready to dig in and start addressing the problem. We want to predict how much each user is going to like all of the movies he or she has not yet read.\n",
    "\n",
    "\n",
    "### Baselines\n",
    "\n",
    "Every good analysis needs some kind of baseline methods to compare against. It's difficult to claim we've produced good results if we have no reference point for what defines \"good\". We'll define three very simple baseline methods and find the RMSE using these methods. Our goal will be to obtain lower RMSE scores with whatever model we produce.\n",
    "\n",
    "#### Uniform Random Baseline\n",
    "\n",
    "Our first baseline is about as dead stupid as you can get. Every place we see a missing value in $R$, we'll simply fill it with a number drawn uniformly at random in the range [1, 5]. We expect this method to do the worst by far.\n",
    "\n",
    "$$R_{ij}^* \\sim Uniform$$\n",
    "\n",
    "#### Global Mean Baseline\n",
    "\n",
    "This method is only slightly better than the last. Wherever we have a missing value, we'll fill it in with the mean of all observed ratings.\n",
    "\n",
    "$$\\text{global_mean} = \\frac{1}{N \\times M} \\sum_{i=1}^N \\sum_{j=1}^M I_{ij}(R_{ij})$$\n",
    "\n",
    "$$R_{ij}^* = \\text{global_mean}$$\n",
    "\n",
    "#### Mean of Means Baseline\n",
    "\n",
    "Now we're going to start getting a bit smarter. We imagine some users might be easily amused, and inclined to rate all movies more highly. Other users might be the opposite. Additionally, some movies might simply be more witty than others, so all users might rate some movies more highly than others in general. We can clearly see this in our graph of the movie means above. We'll attempt to capture these general trends through per-user and per-movie rating means. We'll also incorporate the global mean to smooth things out a bit. So if we see a missing value in cell $R_{ij}$, we'll average the global mean with the mean of $U_i$ and the mean of $V_j$ and use that value to fill it in.\n",
    "\n",
    "$$\\text{user_means} = \\frac{1}{M} \\sum_{j=1}^M I_{ij}(R_{ij})$$\n",
    "\n",
    "$$\\text{movie_means} = \\frac{1}{N} \\sum_{i=1}^N I_{ij}(R_{ij})$$\n",
    "\n",
    "$$R_{ij}^* = \\frac{1}{3} \\left(\\text{user_means}_i + \\text{ movie_means}_j + \\text{ global_mean} \\right)$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a base class with scaffolding for our 3 baselines.\n",
    "\n",
    "def split_title(title):\n",
    "    \"\"\"Change \"BaselineMethod\" to \"Baseline Method\".\"\"\"\n",
    "    words = []\n",
    "    tmp = [title[0]]\n",
    "    for c in title[1:]:\n",
    "        if c.isupper():\n",
    "            words.append(''.join(tmp))\n",
    "            tmp = [c]\n",
    "        else:\n",
    "            tmp.append(c)\n",
    "    words.append(''.join(tmp))\n",
    "    return ' '.join(words)\n",
    "\n",
    "\n",
    "class Baseline():\n",
    "    \"\"\"Calculate baseline predictions.\"\"\"\n",
    "\n",
    "    def __init__(self, train_data):\n",
    "        \"\"\"Simple heuristic-based transductive learning to fill in missing\n",
    "        values in data matrix.\"\"\"\n",
    "        self.predict(train_data.copy())\n",
    "\n",
    "    def predict(self, train_data):\n",
    "        raise NotImplementedError(\n",
    "            'baseline prediction not implemented for base class')\n",
    "\n",
    "    def rmse(self, test_data):\n",
    "        \"\"\"Calculate root mean squared error for predictions on test data.\"\"\"\n",
    "        return rmse(test_data, self.predicted)\n",
    "\n",
    "    def __str__(self):\n",
    "        return split_title(self.__class__.__name__)\n",
    "\n",
    "\n",
    "# Implement the 3 baselines.\n",
    "\n",
    "class UniformRandomBaseline(Baseline):\n",
    "    \"\"\"Fill missing values with uniform random values.\"\"\"\n",
    "\n",
    "    def predict(self, train_data):\n",
    "        nan_mask = np.isnan(train_data)\n",
    "        masked_train = np.ma.masked_array(train_data, nan_mask)\n",
    "        pmin, pmax = masked_train.min(), masked_train.max()\n",
    "        N = nan_mask.sum()\n",
    "        train_data[nan_mask] = np.random.uniform(pmin, pmax, N)\n",
    "        self.predicted = train_data\n",
    "\n",
    "\n",
    "class GlobalMeanBaseline(Baseline):\n",
    "    \"\"\"Fill in missing values using the global mean.\"\"\"\n",
    "\n",
    "    def predict(self, train_data):\n",
    "        nan_mask = np.isnan(train_data)\n",
    "        train_data[nan_mask] = train_data[~nan_mask].mean()\n",
    "        self.predicted = train_data\n",
    "\n",
    "\n",
    "class MeanOfMeansBaseline(Baseline):\n",
    "    \"\"\"Fill in missing values using mean of user/item/global means.\"\"\"\n",
    "\n",
    "    def predict(self, train_data):\n",
    "        nan_mask = np.isnan(train_data)\n",
    "        masked_train = np.ma.masked_array(train_data, nan_mask)\n",
    "        global_mean = masked_train.mean()\n",
    "        user_means = masked_train.mean(axis=1)\n",
    "        item_means = masked_train.mean(axis=0)\n",
    "        self.predicted = train_data.copy()\n",
    "        n, m = train_data.shape\n",
    "        for i in range(n):\n",
    "            for j in range(m):\n",
    "                if np.ma.isMA(item_means[j]):\n",
    "                    self.predicted[i, j] = np.mean(\n",
    "                        (global_mean, user_means[i]))\n",
    "                else:\n",
    "                    self.predicted[i, j] = np.mean(\n",
    "                        (global_mean, user_means[i], item_means[j]))\n",
    "\n",
    "\n",
    "baseline_methods = {}\n",
    "baseline_methods['ur'] = UniformRandomBaseline\n",
    "baseline_methods['gm'] = GlobalMeanBaseline\n",
    "baseline_methods['mom'] = MeanOfMeansBaseline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Users: 943\n",
      "Movies: 1682\n",
      "Sparsity: 0.9369533063577546\n"
     ]
    }
   ],
   "source": [
    "num_users = data.userid.unique().shape[0]\n",
    "num_items = data.itemid.unique().shape[0]\n",
    "sparsity = 1 - len(data) / (num_users * num_items)\n",
    "print(f\"Users: {num_users}\\nMovies: {num_items}\\nSparsity: {sparsity}\")\n",
    "\n",
    "dense_data = data.pivot(index = 'userid', columns ='itemid', values = 'rating').values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probabilistic Matrix Factorization\n",
    "\n",
    "[Probabilistic Matrix Factorization (PMF)](http://papers.nips.cc/paper/3208-probabilistic-matrix-factorization.pdf) [3] is a probabilistic approach to the collaborative filtering problem that takes a Bayesian perspective. The ratings $R$ are modeled as draws from a Gaussian distribution.  The mean for $R_{ij}$ is $U_i V_j^T$. The precision $\\alpha$ is a fixed parameter that reflects the uncertainty of the estimations; the normal distribution is commonly reparameterized in terms of precision, which is the inverse of the variance. Complexity is controlled by placing zero-mean spherical Gaussian priors on $U$ and $V$. In other words, each row of $U$ is drawn from a multivariate Gaussian with mean $\\mu = 0$ and precision which is some multiple of the identity matrix $I$. Those multiples are $\\alpha_U$ for $U$ and $\\alpha_V$ for $V$. So our model is defined by:\n",
    "\n",
    "$\\newcommand\\given[1][]{\\:#1\\vert\\:}$\n",
    "\n",
    "$$\n",
    "P(R \\given U, V, \\alpha^2) = \n",
    "    \\prod_{i=1}^N \\prod_{j=1}^M\n",
    "        \\left[ \\mathcal{N}(R_{ij} \\given U_i V_j^T, \\alpha^{-1}) \\right]^{I_{ij}}\n",
    "$$\n",
    "\n",
    "$$\n",
    "P(U \\given \\alpha_U^2) =\n",
    "    \\prod_{i=1}^N \\mathcal{N}(U_i \\given 0, \\alpha_U^{-1} \\boldsymbol{I})\n",
    "$$\n",
    "\n",
    "$$\n",
    "P(V \\given \\alpha_U^2) =\n",
    "    \\prod_{j=1}^M \\mathcal{N}(V_j \\given 0, \\alpha_V^{-1} \\boldsymbol{I})\n",
    "$$\n",
    "\n",
    "Given small precision parameters, the priors on $U$ and $V$ ensure our latent variables do not grow too far from 0. This prevents overly strong user preferences and item factor compositions from being learned. This is commonly known as complexity control, where the complexity of the model here is measured by the magnitude of the latent variables. Controlling complexity like this helps prevent overfitting, which allows the model to generalize better for unseen data. We must also choose an appropriate $\\alpha$ value for the normal distribution for $R$. So the challenge becomes choosing appropriate values for $\\alpha_U$, $\\alpha_V$, and $\\alpha$. This challenge can be tackled with the soft weight-sharing methods discussed by [Nowland and Hinton, 1992](http://www.cs.toronto.edu/~fritz/absps/sunspots.pdf) [4]. However, for the purposes of this analysis, we will stick to using point estimates obtained from our data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "import logging\n",
    "import theano\n",
    "import scipy as sp\n",
    "\n",
    "\n",
    "# Enable on-the-fly graph computations, but ignore\n",
    "# absence of intermediate test values.\n",
    "theano.config.compute_test_value = 'ignore'\n",
    "\n",
    "# Set up logging.\n",
    "logger = logging.getLogger()\n",
    "logger.setLevel(logging.INFO)\n",
    "\n",
    "\n",
    "class PMF():\n",
    "    \"\"\"Probabilistic Matrix Factorization model using pymc3.\"\"\"\n",
    "\n",
    "    def __init__(self, train, dim, alpha=2, std=0.01, bounds=(1, 5)):\n",
    "        \"\"\"Build the Probabilistic Matrix Factorization model using pymc3.\n",
    "\n",
    "        :param np.ndarray train: The training data to use for learning the model.\n",
    "        :param int dim: Dimensionality of the model; number of latent factors.\n",
    "        :param int alpha: Fixed precision for the likelihood function.\n",
    "        :param float std: Amount of noise to use for model initialization.\n",
    "        :param (tuple of int) bounds: (lower, upper) bound of ratings.\n",
    "            These bounds will simply be used to cap the estimates produced for R.\n",
    "\n",
    "        \"\"\"\n",
    "        self.dim = dim\n",
    "        self.alpha = alpha\n",
    "        self.std = np.sqrt(1.0 / alpha)\n",
    "        self.bounds = bounds\n",
    "        self.data = train.copy()\n",
    "        n, m = self.data.shape\n",
    "\n",
    "        # Perform mean value imputation\n",
    "        nan_mask = np.isnan(self.data)\n",
    "        self.data[nan_mask] = self.data[~nan_mask].mean()\n",
    "\n",
    "        # Low precision reflects uncertainty; prevents overfitting.\n",
    "        # Set to the mean variance across users and items.\n",
    "        self.alpha_u = 1 / self.data.var(axis=1).mean()\n",
    "        self.alpha_v = 1 / self.data.var(axis=0).mean()\n",
    "\n",
    "        # Specify the model.\n",
    "        logging.info('building the PMF model')\n",
    "        with pm.Model() as pmf:\n",
    "            U = pm.MvNormal(\n",
    "                'U', mu=0, tau=self.alpha_u * np.eye(dim),\n",
    "                shape=(n, dim), testval=np.random.randn(n, dim) * std)\n",
    "            V = pm.MvNormal(\n",
    "                'V', mu=0, tau=self.alpha_v * np.eye(dim),\n",
    "                shape=(m, dim), testval=np.random.randn(m, dim) * std)\n",
    "            R = pm.Normal(\n",
    "                'R', mu=(U @ V.T)[~nan_mask], tau=self.alpha,\n",
    "                observed=self.data[~nan_mask])\n",
    "\n",
    "        logging.info('done building the PMF model')\n",
    "        self.model = pmf\n",
    "\n",
    "    def __str__(self):\n",
    "        return self.name"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll also need functions for calculating the MAP and performing sampling on our PMF model. When the observation noise variance $\\alpha$ and the prior variances $\\alpha_U$ and $\\alpha_V$ are all kept fixed, maximizing the log posterior is equivalent to minimizing the sum-of-squared-errors objective function with quadratic regularization terms.\n",
    "\n",
    "$$ E = \\frac{1}{2} \\sum_{i=1}^N \\sum_{j=1}^M I_{ij} (R_{ij} - U_i V_j^T)^2 + \\frac{\\lambda_U}{2} \\sum_{i=1}^N \\|U\\|_{Fro}^2 + \\frac{\\lambda_V}{2} \\sum_{j=1}^M \\|V\\|_{Fro}^2, $$\n",
    "\n",
    "where $\\lambda_U = \\alpha_U / \\alpha$, $\\lambda_V = \\alpha_V / \\alpha$, and $\\|\\cdot\\|_{Fro}^2$ denotes the Frobenius norm [3]. Minimizing this objective function gives a local minimum, which is essentially a maximum a posteriori (MAP) estimate. While it is possible to use a fast Stochastic Gradient Descent procedure to find this MAP, we'll be finding it using the utilities built into `pymc3`. In particular, we'll use `find_MAP` with Powell optimization (`scipy.optimize.fmin_powell`). Having found this MAP estimate, we can use it as our starting point for MCMC sampling.\n",
    "\n",
    "Since it is a reasonably complex model, we expect the MAP estimation to take some time. So let's save it after we've found it. Note that we define a function for finding the MAP below, assuming it will receive a namespace with some variables in it. Then we attach that function to the PMF class, where it will have such a namespace after initialization. The PMF class is defined in pieces this way so I can say a few things between each piece to make it clearer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def _find_map(self):\n",
    "    \"\"\"Find mode of posterior using L-BFGS-B optimization.\"\"\"\n",
    "    tstart = time.time()\n",
    "    with self.model:\n",
    "        logging.info('finding PMF MAP using L-BFGS-B optimization...')\n",
    "        self._map = pm.find_MAP(method='L-BFGS-B')\n",
    "\n",
    "    elapsed = int(time.time() - tstart)\n",
    "    logging.info('found PMF MAP in %d seconds' % elapsed)\n",
    "    return self._map\n",
    "\n",
    "def _map(self):\n",
    "    try:\n",
    "        return self._map\n",
    "    except:\n",
    "        return self.find_map()\n",
    "\n",
    "# Update our class with the new MAP infrastructure.\n",
    "PMF.find_map = _find_map\n",
    "PMF.map = property(_map)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So now our PMF class has a `map` `property` which will either be found using Powell optimization or loaded from a previous optimization. Once we have the MAP, we can use it as a starting point for our MCMC sampler. We'll need a sampling function in order to draw MCMC samples to approximate the posterior distribution of the PMF model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Draw MCMC samples.\n",
    "def _draw_samples(self, **kwargs):\n",
    "    kwargs.setdefault('chains', 1)\n",
    "    with self.model:\n",
    "        self.trace = pm.sample(**kwargs)\n",
    "        \n",
    "# Update our class with the sampling infrastructure.\n",
    "PMF.draw_samples = _draw_samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could define some kind of default trace property like we did for the MAP, but that would mean using possibly nonsensical values for `nsamples` and `cores`. Better to leave it as a non-optional call to `draw_samples`. Finally, we'll need a function to make predictions using our inferred values for $U$ and $V$. For user $i$ and movie $j$, a prediction is generated by drawing from $\\mathcal{N}(U_i V_j^T, \\alpha)$. To generate predictions from the sampler, we generate an $R$ matrix for each $U$ and $V$ sampled, then we combine these by averaging over the $K$ samples.\n",
    "\n",
    "$$\n",
    "P(R_{ij}^* \\given R, \\alpha, \\alpha_U, \\alpha_V) \\approx\n",
    "    \\frac{1}{K} \\sum_{k=1}^K \\mathcal{N}(U_i V_j^T, \\alpha)\n",
    "$$\n",
    "\n",
    "We'll want to inspect the individual $R$ matrices before averaging them for diagnostic purposes. So we'll write code for the averaging piece during evaluation. The function below simply draws an $R$ matrix given a $U$ and $V$ and the fixed $\\alpha$ stored in the PMF object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def _predict(self, U, V):\n",
    "    \"\"\"Estimate R from the given values of U and V.\"\"\"\n",
    "    R = np.dot(U, V.T)\n",
    "    n, m = R.shape\n",
    "    sample_R = np.random.normal(R, self.std)\n",
    "    # bound ratings\n",
    "    low, high = self.bounds\n",
    "    sample_R[sample_R < low] = low\n",
    "    sample_R[sample_R > high] = high\n",
    "    return sample_R\n",
    "\n",
    "\n",
    "PMF.predict = _predict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One final thing to note: the dot products in this model are often constrained using a logistic function $g(x) = 1/(1 + exp(-x))$, that bounds the predictions to the range [0, 1]. To facilitate this bounding, the ratings are also mapped to the range [0, 1] using $t(x) = (x + min) / range$. The authors of PMF also introduced a constrained version which performs better on users with less ratings [3]. Both models are generally improvements upon the basic model presented here. However, in the interest of time and space, these will not be implemented here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation\n",
    "\n",
    "### Metrics\n",
    "\n",
    "In order to understand how effective our models are, we'll need to be able to evaluate them. We'll be evaluating in terms of root mean squared error (RMSE), which looks like this:\n",
    "\n",
    "$$\n",
    "RMSE = \\sqrt{ \\frac{ \\sum_{i=1}^N \\sum_{j=1}^M I_{ij} (R_{ij} - R_{ij}^*)^2 }\n",
    "                   { \\sum_{i=1}^N \\sum_{j=1}^M I_{ij} } }\n",
    "$$\n",
    "\n",
    "In this case, the RMSE can be thought of as the standard deviation of our predictions from the actual user preferences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define our evaluation function.\n",
    "def rmse(test_data, predicted):\n",
    "    \"\"\"Calculate root mean squared error.\n",
    "    Ignoring missing values in the test data.\n",
    "    \"\"\"\n",
    "    I = ~np.isnan(test_data)   # indicator for missing values\n",
    "    N = I.sum()                # number of non-missing values\n",
    "    sqerror = abs(test_data - predicted) ** 2  # squared error array\n",
    "    mse = sqerror[I].sum() / N                 # mean squared error\n",
    "    return np.sqrt(mse)                        # RMSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training Data vs. Test Data\n",
    "\n",
    "The next thing we need to do is split our data into a training set and a test set. Matrix factorization techniques use [transductive learning](http://en.wikipedia.org/wiki/Transduction_%28machine_learning%29) rather than inductive learning. So we produce a test set by taking a random sample of the cells in the full $N \\times M$ data matrix. The values selected as test samples are replaced with `nan` values in a copy of the original data matrix to produce the training set. Since we'll be producing random splits, let's also write out the train/test sets generated. This will allow us to replicate our results. We'd like to be able to idenfity which split is which, so we'll take a hash of the indices selected for testing and use that to save the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a function for splitting train/test data.\n",
    "def split_train_test(data, percent_test=0.1):\n",
    "    \"\"\"Split the data into train/test sets.\n",
    "    :param int percent_test: Percentage of data to use for testing. Default 10.\n",
    "    \"\"\"\n",
    "    n, m = data.shape             # # users, # movies\n",
    "    N = n * m                     # # cells in matrix\n",
    "\n",
    "    # Prepare train/test ndarrays.\n",
    "    train = data.copy()\n",
    "    test = np.ones(data.shape) * np.nan\n",
    "\n",
    "    # Draw random sample of training data to use for testing.\n",
    "    tosample = np.where(~np.isnan(train))       # ignore nan values in data\n",
    "    idx_pairs = list(zip(tosample[0], tosample[1]))   # tuples of row/col index pairs\n",
    "    \n",
    "    test_size = int(len(idx_pairs) * percent_test)  # use 10% of data as test set\n",
    "    train_size = len(idx_pairs) - test_size   # and remainder for training\n",
    "    \n",
    "    indices = np.arange(len(idx_pairs))         # indices of index pairs\n",
    "    sample = np.random.choice(indices, replace=False, size=test_size)\n",
    "\n",
    "    # Transfer random sample from train set to test set.\n",
    "    for idx in sample:\n",
    "        idx_pair = idx_pairs[idx]\n",
    "        test[idx_pair] = train[idx_pair]  # transfer to test set\n",
    "        train[idx_pair] = np.nan          # remove from train set\n",
    "\n",
    "    # Verify everything worked properly\n",
    "    assert(train_size == N-np.isnan(train).sum())\n",
    "    assert(test_size == N-np.isnan(test).sum())\n",
    "    \n",
    "    # Return train set and test set\n",
    "    return train, test\n",
    "\n",
    "train, test = split_train_test(dense_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uniform Random Baseline RMSE:\t1.68522\n",
      "Global Mean Baseline RMSE:\t1.12244\n",
      "Mean Of Means Baseline RMSE:\t1.01263\n"
     ]
    }
   ],
   "source": [
    "# Let's see the results:\n",
    "baselines = {}\n",
    "for name in baseline_methods:\n",
    "    Method = baseline_methods[name]\n",
    "    method = Method(train)\n",
    "    baselines[name] = method.rmse(test)\n",
    "    print('%s RMSE:\\t%.5f' % (method, baselines[name]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected: the uniform random baseline is the worst by far, the global mean baseline is next best, and the mean of means method is our best baseline. Now let's see how PMF stacks up."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:root:building the PMF model\n",
      "/home/zv/upstream/mc4/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n",
      "INFO:root:done building the PMF model\n"
     ]
    }
   ],
   "source": [
    "# We use a fixed precision for the likelihood.\n",
    "# This reflects uncertainty in the dot product.\n",
    "# We choose 2 in the footsteps Salakhutdinov\n",
    "# Mnihof.\n",
    "ALPHA = 2\n",
    "\n",
    "# The dimensionality D; the number of latent factors.\n",
    "# We can adjust this higher to try to capture more subtle\n",
    "# characteristics of each movie. However, the higher it is,\n",
    "# the more expensive our inference procedures will be.\n",
    "# Specifically, we have D(N + M) latent variables. For our\n",
    "# Movielens dataset, this means we have D(2625), so for 5\n",
    "# dimensions, we are sampling 13125 latent variables.\n",
    "DIM = 10\n",
    "\n",
    "\n",
    "pmf = PMF(train, DIM, ALPHA, std=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predictions Using MAP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:root:finding PMF MAP using L-BFGS-B optimization...\n",
      "  0%|          | 0/5000 [00:00<?, ?it/s]/home/zv/upstream/mc4/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n",
      "logp = -1.5355e+05, ||grad|| = 0.7578: 100%|██████████| 481/481 [00:13<00:00, 35.20it/s]    \n",
      "INFO:root:found PMF MAP in 17 seconds\n"
     ]
    }
   ],
   "source": [
    "# Find MAP for PMF.\n",
    "pmf.find_map();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Excellent. The first thing we want to do is make sure the MAP estimate we obtained is reasonable. We can do this by computing RMSE on the predicted ratings obtained from the MAP values of $U$ and $V$. First we define a function for generating the predicted ratings $R$ from $U$ and $V$. We ensure the actual rating bounds are enforced by setting all values below 1 to 1 and all values above 5 to 5. Finally, we compute RMSE for both the training set and the test set. We expect the test RMSE to be higher. The difference between the two gives some idea of how much we have overfit. Some difference is always expected, but a very low RMSE on the training set with a high RMSE on the test set is a definite sign of overfitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def eval_map(pmf_model, train, test):\n",
    "    U = pmf_model.map['U']\n",
    "    V = pmf_model.map['V']\n",
    "    \n",
    "    # Make predictions and calculate RMSE on train & test sets.\n",
    "    predictions = pmf_model.predict(U, V)\n",
    "    train_rmse = rmse(train, predictions)\n",
    "    test_rmse = rmse(test, predictions)\n",
    "    overfit = test_rmse - train_rmse\n",
    "    \n",
    "    # Print report.\n",
    "    print('PMF MAP training RMSE: %.5f' % train_rmse)\n",
    "    print('PMF MAP testing RMSE:  %.5f' % test_rmse)\n",
    "    print('Train/test difference: %.5f' % overfit)\n",
    "    \n",
    "    return test_rmse\n",
    "    \n",
    "\n",
    "# Add eval function to PMF class.\n",
    "PMF.eval_map = eval_map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PMF MAP training RMSE: 1.01383\n",
      "PMF MAP testing RMSE:  1.14452\n",
      "Train/test difference: 0.13070\n",
      "PMF MAP Improvement:   -0.13190\n"
     ]
    }
   ],
   "source": [
    "# Evaluate PMF MAP estimates.\n",
    "pmf_map_rmse = pmf.eval_map(train, test)\n",
    "pmf_improvement = baselines['mom'] - pmf_map_rmse\n",
    "print('PMF MAP Improvement:   %.5f' % pmf_improvement)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We actually see a decrease in performance between the MAP estimate and the mean of means performance. We also have a fairly large difference in the RMSE values between the train and the test sets. This indicates that the point estimates for $\\alpha_U$ and $\\alpha_V$ that we calculated from our data are not doing a great job of controlling model complexity. \n",
    "\n",
    "Let's see if we can improve our estimates by approximating our posterior distribution with MCMC sampling. We'll draw 500 samples, with 500 tuning samples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predictions using MCMC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "INFO:pymc3:Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "INFO:pymc3:Initializing NUTS using jitter+adapt_diag...\n",
      "/home/zv/upstream/mc4/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n",
      "Sequential sampling (1 chains in 1 job)\n",
      "INFO:pymc3:Sequential sampling (1 chains in 1 job)\n",
      "NUTS: [V, U]\n",
      "INFO:pymc3:NUTS: [V, U]\n",
      "Sampling chain 0, 0 divergences: 100%|██████████| 1000/1000 [28:37<00:00,  1.72s/it]\n",
      "Only one chain was sampled, this makes it impossible to run some convergence checks\n",
      "INFO:pymc3:Only one chain was sampled, this makes it impossible to run some convergence checks\n"
     ]
    }
   ],
   "source": [
    "# Draw MCMC samples.\n",
    "pmf.draw_samples(draws=500, tune=500, )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Diagnostics and Posterior Predictive Check\n",
    "\n",
    "The next step is to check how many samples we should discard as burn-in. Normally, we'd do this using a traceplot to get some idea of where the sampled variables start to converge. In this case, we have high-dimensional samples, so we need to find a way to approximate them. One way was proposed by [Salakhutdinov and Mnih, p.886](https://www.cs.toronto.edu/~amnih/papers/bpmf.pdf). We can calculate the Frobenius norms of $U$ and $V$ at each step and monitor those for convergence. This essentially gives us some idea when the average magnitude of the latent variables is stabilizing. The equations for the Frobenius norms of $U$ and $V$ are shown below. We will use `numpy`'s `linalg` package to calculate these.\n",
    "\n",
    "$$ \\|U\\|_{Fro}^2 = \\sqrt{\\sum_{i=1}^N \\sum_{d=1}^D |U_{id}|^2}, \\hspace{40pt} \\|V\\|_{Fro}^2 = \\sqrt{\\sum_{j=1}^M \\sum_{d=1}^D |V_{jd}|^2} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def _norms(pmf_model, monitor=('U', 'V'), ord='fro'):\n",
    "    \"\"\"Return norms of latent variables at each step in the\n",
    "    sample trace. These can be used to monitor convergence\n",
    "    of the sampler.\n",
    "    \"\"\"\n",
    "    monitor = ('U', 'V')\n",
    "    norms = {var: [] for var in monitor}\n",
    "    for sample in pmf_model.trace:\n",
    "        for var in monitor:\n",
    "            norms[var].append(np.linalg.norm(sample[var], ord))\n",
    "    return norms\n",
    "\n",
    "\n",
    "def _traceplot(pmf_model):\n",
    "    \"\"\"Plot Frobenius norms of U and V as a function of sample #.\"\"\"\n",
    "    trace_norms = pmf_model.norms()\n",
    "    u_series = pd.Series(trace_norms['U'])\n",
    "    v_series = pd.Series(trace_norms['V'])\n",
    "    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 7))\n",
    "    u_series.plot(kind='line', ax=ax1, grid=False,\n",
    "                  title=\"$\\|U\\|_{Fro}^2$ at Each Sample\")\n",
    "    v_series.plot(kind='line', ax=ax2, grid=False,\n",
    "                  title=\"$\\|V\\|_{Fro}^2$ at Each Sample\")\n",
    "    ax1.set_xlabel(\"Sample Number\")\n",
    "    ax2.set_xlabel(\"Sample Number\")\n",
    "    \n",
    "    \n",
    "PMF.norms = _norms\n",
    "PMF.traceplot = _traceplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x504 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf.traceplot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It appears we get convergence of $U$ and $V$ after about the default tuning. When testing for convergence, we also want to see convergence of the particular statistics we are looking for, since different characteristics of the posterior may converge at different rates. Let's also do a traceplot of the RSME. We'll compute RMSE for both the train and the test set, even though the convergence is indicated by RMSE on the training set alone. In addition, let's compute a running RMSE on the train/test sets to see how aggregate performance improves or decreases as we continue to sample.\n",
    "\n",
    "Notice here that we are sampling from 1 chain only, which makes the convergence statisitcs like $\\hat{r}$ impossible (we can still compute the split-rhat but the purpose is different). The reason of not sampling multiple chain is that PMF might not have unique solution. Thus without constraints, the solutions are at best symmetrical, at worse identical under any rotation, in any case subject to label switching. In fact if we sample from multiple chains we will see large $\\hat{r}$ indicating the sampler is exploring different solutions in different part of parameter space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def _running_rmse(pmf_model, test_data, train_data, burn_in=0, plot=True):\n",
    "    \"\"\"Calculate RMSE for each step of the trace to monitor convergence.\n",
    "    \"\"\"\n",
    "    burn_in = burn_in if len(pmf_model.trace) >= burn_in else 0\n",
    "    results = {'per-step-train': [], 'running-train': [],\n",
    "               'per-step-test': [], 'running-test': []}\n",
    "    R = np.zeros(test_data.shape)\n",
    "    for cnt, sample in enumerate(pmf_model.trace[burn_in:]):\n",
    "        sample_R = pmf_model.predict(sample['U'], sample['V'])\n",
    "        R += sample_R\n",
    "        running_R = R / (cnt + 1)\n",
    "        results['per-step-train'].append(rmse(train_data, sample_R))\n",
    "        results['running-train'].append(rmse(train_data, running_R))\n",
    "        results['per-step-test'].append(rmse(test_data, sample_R))\n",
    "        results['running-test'].append(rmse(test_data, running_R))\n",
    "    \n",
    "    results = pd.DataFrame(results)\n",
    "\n",
    "    if plot:\n",
    "        results.plot(\n",
    "            kind='line', grid=False, figsize=(15, 7),\n",
    "            title='Per-step and Running RMSE From Posterior Predictive')\n",
    "        \n",
    "    # Return the final predictions, and the RMSE calculations\n",
    "    return running_R, results\n",
    "\n",
    "\n",
    "PMF.running_rmse = _running_rmse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predicted, results = pmf.running_rmse(test, train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Posterior predictive train RMSE: 0.77956\n",
      "Posterior predictive test RMSE:  0.92176\n",
      "Train/test difference:           0.14220\n",
      "Improvement from MAP:            0.22276\n",
      "Improvement from Mean of Means:  0.09086\n"
     ]
    }
   ],
   "source": [
    "# And our final RMSE?\n",
    "final_test_rmse = results['running-test'].values[-1]\n",
    "final_train_rmse = results['running-train'].values[-1]\n",
    "print('Posterior predictive train RMSE: %.5f' % final_train_rmse)\n",
    "print('Posterior predictive test RMSE:  %.5f' % final_test_rmse)\n",
    "print('Train/test difference:           %.5f' % (final_test_rmse - final_train_rmse))\n",
    "print('Improvement from MAP:            %.5f' % (pmf_map_rmse - final_test_rmse))\n",
    "print('Improvement from Mean of Means:  %.5f' % (baselines['mom'] - final_test_rmse))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have some interesting results here. As expected, our MCMC sampler provides lower error on the training set. However, it seems it does so at the cost of overfitting the data. This results in a decrease in test RMSE as compared to the MAP, even though it is still much better than our best baseline. So why might this be the case? Recall that we used point estimates for our precision paremeters $\\alpha_U$ and $\\alpha_V$ and we chose a fixed precision $\\alpha$. It is quite likely that by doing this, we constrained our posterior in a way that biased it towards the training data. In reality, the variance in the user ratings and the movie ratings is unlikely to be equal to the means of sample variances we used. Also, the most reasonable observation precision $\\alpha$ is likely different as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have some interesting results here. As expected, our MCMC sampler provides lower error on the training set. However, it seems it does so at the cost of overfitting the data. This results in a decrease in test RMSE as compared to the MAP, even though it is still much better than our best baseline. So why might this be the case? Recall that we used point estimates for our precision paremeters $\\alpha_U$ and $\\alpha_V$ and we chose a fixed precision $\\alpha$. It is quite likely that by doing this, we constrained our posterior in a way that biased it towards the training data. In reality, the variance in the user ratings and the movie ratings is unlikely to be equal to the means of sample variances we used. Also, the most reasonable observation precision $\\alpha$ is likely different as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have some interesting results here. As expected, our MCMC sampler provides lower error on the training set. However, it seems it does so at the cost of overfitting the data. This results in a decrease in test RMSE as compared to the MAP, even though it is still much better than our best baseline. So why might this be the case? Recall that we used point estimates for our precision paremeters $\\alpha_U$ and $\\alpha_V$ and we chose a fixed precision $\\alpha$. It is quite likely that by doing this, we constrained our posterior in a way that biased it towards the training data. In reality, the variance in the user ratings and the movie ratings is unlikely to be equal to the means of sample variances we used. Also, the most reasonable observation precision $\\alpha$ is likely different as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary of Results\n",
    "\n",
    "Let's summarize our results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = 100  # RMSE doesn't really change after 100th sample anyway.\n",
    "all_results = pd.DataFrame({\n",
    "    'uniform random': np.repeat(baselines['ur'], size),\n",
    "    'global means': np.repeat(baselines['gm'], size),\n",
    "    'mean of means': np.repeat(baselines['mom'], size),\n",
    "    'PMF MAP': np.repeat(pmf_map_rmse, size),\n",
    "    'PMF MCMC': results['running-test'][:size],\n",
    "})\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "all_results.plot(kind='line', grid=False, ax=ax,\n",
    "                 title='RMSE for all methods')\n",
    "ax.set_xlabel(\"Number of Samples\")\n",
    "ax.set_ylabel(\"RMSE\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "We set out to predict user preferences for unseen movies. First we discussed the intuitive notion behind the user-user and item-item neighborhood approaches to collaborative filtering. Then we formalized our intuitions. With a firm understanding of our problem context, we moved on to exploring our subset of the Movielens data. After discovering some general patterns, we defined three baseline methods: uniform random, global mean, and mean of means. With the goal of besting our baseline methods, we implemented the basic version of Probabilistic Matrix Factorization (PMF) using `pymc3`.\n",
    "\n",
    "Our results demonstrate that the mean of means method is our best baseline on our prediction task. As expected, we are able to obtain a significant decrease in RMSE using the PMF MAP estimate obtained via Powell optimization. We illustrated one way to monitor convergence of an MCMC sampler with a high-dimensionality sampling space using the Frobenius norms of the sampled variables. The traceplots using this method seem to indicate that our sampler converged to the posterior. Results using this posterior showed that attempting to improve the MAP estimation using MCMC sampling actually overfit the training data and increased test RMSE. This was likely caused by the constraining of the posterior via fixed precision parameters $\\alpha$, $\\alpha_U$, and $\\alpha_V$.\n",
    "\n",
    "As a followup to this analysis, it would be interesting to also implement the logistic and constrained versions of PMF. We expect both models to outperform the basic PMF model. We could also implement the [fully Bayesian version of PMF](https://www.cs.toronto.edu/~amnih/papers/bpmf.pdf) (BPMF), which places hyperpriors on the model parameters to automatically learn ideal mean and precision parameters for $U$ and $V$. This would likely resolve the issue we faced in this analysis. We would expect BPMF to improve upon the MAP estimation produced here by learning more suitable hyperparameters and parameters. For a basic (but working!) implementation of BPMF in `pymc3`, see [this gist](https://gist.github.com/macks22/00a17b1d374dfc267a9a).\n",
    "\n",
    "If you made it this far, then congratulations! You now have some idea of how to build a basic recommender system. These same ideas and methods can be used on many different recommendation tasks. Items can be movies, products, advertisements, courses, or even other people. Any time you can build yourself a user-item matrix with user preferences in the cells, you can use these types of collaborative filtering algorithms to predict the missing values. If you want to learn more about recommender systems, the first reference is a good place to start."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "1.  Y. Koren, R. Bell, and C. Volinsky, “Matrix Factorization Techniques for Recommender Systems,” Computer, vol. 42, no. 8, pp. 30–37, Aug. 2009.\n",
    "2.  K. Goldberg, T. Roeder, D. Gupta, and C. Perkins, “Eigentaste: A constant time collaborative filtering algorithm,” Information Retrieval, vol. 4, no. 2, pp. 133–151, 2001.\n",
    "3.  A. Mnih and R. Salakhutdinov, “Probabilistic matrix factorization,” in Advances in neural information processing systems, 2007, pp. 1257–1264.\n",
    "4.  S. J. Nowlan and G. E. Hinton, “Simplifying Neural Networks by Soft Weight-sharing,” Neural Comput., vol. 4, no. 4, pp. 473–493, Jul. 1992.\n",
    "5.  R. Salakhutdinov and A. Mnih, “Bayesian Probabilistic Matrix Factorization Using Markov Chain Monte Carlo,” in Proceedings of the 25th International Conference on Machine Learning, New York, NY, USA, 2008, pp. 880–887.\n",
    "\n",
    "\n",
    "The model discussed in this analysis was developed by Ruslan Salakhutdinov and Andriy Mnih. Code and supporting text are the original work of [Mack Sweeney](https://www.linkedin.com/in/macksweeney) with changes made to adapt the code and text for the Movielens dataset by Colin Carroll and Rob Zinkov.\n",
    "\n",
    "\n"
   ]
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